Suggest models for prediction based on small sample data I am not a traditional statistics guy. I am from an electrical engineering background. So, spare me for lack of jargon.
The model is to be used for predicting agricultural output based on previous data. One method is Grey model prediction, which need around 4 to 8 sample data for prediction. Could you think of any other model?
E.g.: I have national agriculture output of sugarcane from 1996 to 2010 on an annual basis. That accounts for 15 data. Now using these data, I wish to design a prediction model and use it to forecast the next 2 or 3 years of national production output of sugarcane.
My confusion is about which model will give me the best forecasting result for such a small amount of data.
Please let me know anything else is lacking in the description.
Thanks.
 A: You are looking for time series forecasting. I recommend this free textbook.
Histories of 15 yearly data points are not uncommon in time series forecasting. For instance, the very first one of the series used in the classical M3 competition has only 14 data points. Let's use R and look at this dataset.
library(Mcomp)
M3[[1]]
M3[[1]]$x

We can fit an Exponential Smoothing model using ets() (for "Error, Trend, Seasonality"), which attempts to automatically choose the correct model in terms of trend, seasonality and error - seasonality is irrelevant for yearly data. Let's forecast using this model. forecast() will give us a point forecast as well as (by default) 80% and 95% prediction intervals. We can also plot the original series, the point forecasts and the prediction intervals.
ets.model <- ets(M3[[1]]$x)
forecast(ets.model,h=3)
plot(forecast(ets.model,h=3))


Similarly, auto.arima() will try to fit the best ARIMA model:
arima.model <- auto.arima(M3[[1]]$x)
forecast(arima.model,h=3)
plot(forecast(arima.model,h=3))


The textbook I linked to above will bring you up to speed on both Exponential Smoothing and ARIMA, as well as other aspects of forecasting, like model selection and accuracy measurement. As I noted in my comment above, I don't know a "Grey model", and after a couple of years in this field, I would rather suggest using standard methods like Exponential Smoothing and ARIMA than an unknown method - after all, there are reasons why these methods have evolved to be the mainstay in time series forecasting.
Happy forecasting!
